Neighborhood sequences in the diamond grid: Algorithms with two and three neighbors

Nagy, Benedek; Strand, Robin

doi:10.1002/ima.20182

Cited by 9 publications

(6 citation statements)

References 23 publications

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“…Similar results for other kinds of grids are also known, see e.g. [8] (nD hexagonal grids), [9] (diamond grid) and [10] (general point grids) and the references given there.…”

Section: Introductionsupporting

confidence: 78%

“…Similar results for other kinds of grids are also known, see e.g. [8] (nD hexagonal grids), [9] (diamond grid) and [10] (general point grids) and the references given there. Classical chamfer distances using 3 × 3, 5 × 5 and 7 × 7 neighborhoods given by Borgefors [1,2] are generated by the masks respectively (with the actual generator entries underlined).…”

Section: Introductionsupporting

confidence: 78%

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Approximation of the Euclidean Distance by Chamfer Distances

Hajdú¹,

Hajdu²,

Tijdeman³

2012

Acta Cybern

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Chamfer distances play an important role in the theory of distance transforms. Though the determination of the exact Euclidean distance transform is also a well investigated area, the classical chamfering method based upon "small" neighborhoods still outperforms it e.g. in terms of computation time. In this paper we determine the best possible maximum relative error of chamfer distances under various boundary conditions. In each case some best approximating sequences are explicitly given. Further, because of possible practical interest, we give all best approximating sequences in case of small (i.e. 5 × 5 and 7 × 7) neighborhoods.

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“…Similar results for other kinds of grids are also known, see e.g. [8] (nD hexagonal grids), [9] (diamond grid) and [10] (general point grids) and the references given there.…”

Section: Introductionsupporting

confidence: 78%

Section: Introductionsupporting

confidence: 78%

Approximation of the Euclidean Distance by Chamfer Distances

Hajdú¹,

Hajdu²,

Tijdeman³

2012

Acta Cybern

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“…This is a very regular structure, and minimum in the sense that one requires 4 directions to form a 3D structure (as 4 points are required to produce the simplest 3D body, the tetrahedron). In References 32,33, when distances are calculated using Voronoi neighbors of the voxel representation of the grid, the positions of the carbon atoms were addressed using integer triplets. The diamond grid, however, is not a point lattice and is not invariant under translations with any grid vector, so, for example, translating the structure by the vector of two neighbor points will not map all of the grid points into grid points.…”

Section: Introductionmentioning

confidence: 99%

The hyper‐Wiener Index of diamond nanowires

Nagy

2023

Int J of Quantum Chemistry

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Carbon nanowires based on various structures have various applications. In this article, our focus is on diamond nano‐wires, based on the structure of the diamond. Our goal is to characterize these nanowires by providing their hyper‐Wiener index, one of the basic topological graph indices. The diamond is formed by carbon atoms in a compact structure: every atom has exactly four neighbors connected by covalent bonds according to the simplest three‐dimensional polyhedron. Considering an atom in the center of a tetrahedron, its neighbors, the atoms connected to it by bonds, are located in the corners of the tetrahedron. In this article, this “diamond‐grid” structure is analysed in the case that the graphs correspond to connected parts of sequences of unit cells, in this way forming nanowires of various lengths. By a combinatorial approach, a closed formula is proven for the hyper‐Wiener index based on the graph‐distances of every pair of carbon atoms (i.e., the minimal number of edges connecting the atoms), and this formula depends only on the size of the graph in terms of the number of unit cells included.

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“…However, in recent times, non standard, three-dimensional grids received a lot of interest, particularly with applications in networks [35], image processing [15,27,36], computer vision [17], and many other fields. Among non standard grids we can cite face-centered cubic (FCC), body-centered cubic (BCC), honeycomb [8], and diamond grids [32].…”

Section: Introductionmentioning

confidence: 99%

Digital Objects in Rhombic Dodecahedron Grid

Biswas

Largeteau-Skapin

Zrour

et al. 2020

Mathematical Morphology - Theory and Applications

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Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system.

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Neighborhood sequences in the diamond grid: Algorithms with two and three neighbors

Cited by 9 publications

References 23 publications

Approximation of the Euclidean Distance by Chamfer Distances

Approximation of the Euclidean Distance by Chamfer Distances

The hyper‐Wiener Index of diamond nanowires

Digital Objects in Rhombic Dodecahedron Grid

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